Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Show that the angle sum of any quadrilateral is 27.

Show that the angle sum of any quadrilateral is 27.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.2: Indirect Proof
Problem 11E: Which of the following statements would you prove by the indirect method? a In triangle ABC, if...
See similar textbooks
icon
Related questions
Question
ometry of N and M, not s line equals M. is unique. el to L through ed ASA ("angle shown in Fig- least one side y between L e point where etermined by But then an ence Land assumption that there is d M are in ollow from clid's par- it, so the , there is om," af- book in it does en need ate in- n such mply gle, 2.1 The parallel axiom To prove this property, draw a line L through one vertex of the trian- gle, parallel to the opposite side, as shown in Figure 2.3. L a a В Deduce from only for n = 3,4,6. Y 23 Y Figure 2.3: The angle sum of a triangle Then the angle on the left beneath L is alternate to the angle a in the triangle, so it is equal to a. Similarly, the angle on the right beneath Lis equal to y. But then the straight angle л beneath Lequals a+B+y, the angle sum of the triangle. Exercises The triangle is the most important polygon, because any polygon can be built from triangles. For example, the angle sum of any quadrilateral (polygon with four sides) can be worked out by cutting the quadrilateral into two triangles. Show that the angle sum of any quadrilateral is 27. A polygon P is called convex if the line segment between any two points in P lies entirely in P. For these polygons, it is also easy to find the angle sum. Explain why a convex n-gon can be cut into n - 2 triangles. Use the dissection of the n-gon into triangles to show that the angle sum of a convex n-gon is (n − 2). to find the angle at each vertex of a regular n-gon (an n-gon with equal sides and equal angles). that copies of a regular n-gon can tile the plane
Transcribed Image Text:ometry of N and M, not s line equals M. is unique. el to L through ed ASA ("angle shown in Fig- least one side y between L e point where etermined by But then an ence Land assumption that there is d M are in ollow from clid's par- it, so the , there is om," af- book in it does en need ate in- n such mply gle, 2.1 The parallel axiom To prove this property, draw a line L through one vertex of the trian- gle, parallel to the opposite side, as shown in Figure 2.3. L a a В Deduce from only for n = 3,4,6. Y 23 Y Figure 2.3: The angle sum of a triangle Then the angle on the left beneath L is alternate to the angle a in the triangle, so it is equal to a. Similarly, the angle on the right beneath Lis equal to y. But then the straight angle л beneath Lequals a+B+y, the angle sum of the triangle. Exercises The triangle is the most important polygon, because any polygon can be built from triangles. For example, the angle sum of any quadrilateral (polygon with four sides) can be worked out by cutting the quadrilateral into two triangles. Show that the angle sum of any quadrilateral is 27. A polygon P is called convex if the line segment between any two points in P lies entirely in P. For these polygons, it is also easy to find the angle sum. Explain why a convex n-gon can be cut into n - 2 triangles. Use the dissection of the n-gon into triangles to show that the angle sum of a convex n-gon is (n − 2). to find the angle at each vertex of a regular n-gon (an n-gon with equal sides and equal angles). that copies of a regular n-gon can tile the plane
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS